Algorithm Speedup

Memory limit: 64 MB

As a punishment for misbehaving, Byteasar is to calculate a certain mysterious and nasty Boolean-valued function , which is defined for a pair of positive integer sequences , as follows:

boolean

Where:

• denotes the set of members of the sequence (order and repetitions of elements are insignificant),
• denotes the longest prefix (initial part of any length) of the sequence , such that ,
• denotes the longest suffix (final part of any length) of the sequence , such that ,
• denotes the logical conjunction, - true, - false, and - cardinality of set .

Write a programme that reads several pairs of sequences from the standard input and prints out the values on the standard output for every input pair.

Input

The first line of the standard input contains one integer () denoting the number of sequence pairs to analyse. Next line hold descriptions of test cases. The first line of each description contains two integers and () separated by a single space and denoting the lengths of the first and second sequence, respectively. The second line holds integers () that form the sequence , separated by single spaces. The third line holds integers (), that form the sequence , separated by single spaces.

Output

The output should consist of exactly lines; the -th line (for ) should contain a single integer - 0 or 1 - the value of for -th test case.

Example

For the input data:

2
4 5
3 1 2 1
1 3 1 2 1
7 7
1 1 2 1 2 1 3
1 1 2 1 3 1 3

the correct result is:

0
1

Task authors: Jakub Radoszewski and Wojciech Rytter.